Construction of maximin distance Latin squares and related Latin hypercube designs. (28th February 2017)

• Record Type: Journal Article
• Authors: Xiao, Qian; Xu, Hongquan
• Is Part Of: Biometrika. Volume 104:Number 2(2017)
• Page Start: 455
• Page End: 464
• Publication Date: 2017-02-28
• Subjects: Computer experiment -- Costas array -- Cyclic design -- Maximin distance design -- Space-filling design; Biometry -- Periodicals; 570.1519505
• DOI: 10.1093/biomet/asx006
• Languages: English
• ISSNs: 0006-3444

Abstract

Summary : Maximin distance Latin hypercube designs are widely used in computer experiments, yet their construction is challenging. Based on number theory and finite fields, we propose three algebraic methods to construct maximin distance Latin squares as special Latin hypercube designs. We develop lower bounds on their minimum distances. The resulting Latin squares and related Latin hypercube designs have larger minimum distances than existing ones, and are especially appealing for high-dimensional applications.